The invention relates to a cone pulley such as has become known from German Published application DE-OS 2 459 258. Such a pulley is used as a self-tensioning belt pulley, control pulley or the like for a transmission with strand-like tensioning means such as cone or V-belts. The cone pulley is formed of at least two pulley parts displaceable axially relative to one another, the two pulley parts holding or gripping the strand-like tensioning means therebetween and being biased to a closed position.